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Warm-up

8.5 Indirect Measurement and Additional Similarity Theorems. Warm-up. Solve for x 1. 2. 10. x. 12. x-3. 4. x+1. x. x+6. Section 8-5 Similarity Theorems. 1. Find x. 40. 36. 65. x. 2. Find x. A. x. 75. E. B. 25. D. C. 90.

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Warm-up

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  1. 8.5 Indirect Measurement and Additional Similarity Theorems Warm-up Solve for x 1. 2. 10 x 12 x-3 4 x+1 x x+6

  2. Section 8-5 Similarity Theorems

  3. 1. Find x 40 36 65 x

  4. 2. Find x A x 75 E B 25 D C 90

  5. 8.5 Indirect Measurement and Additional Similarity Theorems Theorems Proportional Altitudes Theorem: If two triangles are similar, then their corresponding altitudes have the same ratio as their corresponding sides.

  6. 3. Given the triangles are similar, solve for x 6 4 9 6 5.25 x

  7. 8.5 Indirect Measurement and Additional Similarity Theorems Theorems Proportional Medians Theorem: If two triangles are similar, then their corresponding medians have the same ratio as their corresponding sides.

  8. 4. Solve for x 12 x 5 4 9 7

  9. 8.5 Indirect Measurement and Additional Similarity Theorems Theorems Proportional Angle Bisectors Theorem: If two triangles are similar, then their corresponding angle bisectors have the same ratio as their corresponding sides.

  10. 105  40x = 7875  x = 196.9 = x 40 75 8.5 Indirect Measurement and Additional Similarity Theorems 5. Estimate the width of the lake.

  11. 12 8  12x = 72  x = 6 feet = 9 x 8.5 Indirect Measurement and Additional Similarity Theorems 6. These triangles are similar. Find x.

  12. 8.5 Indirect Measurement and Additional Similarity Theorems • Given angle A and angle B are right angles • Prove: C B A D E

  13. Assignment Page 537 # 5-20, 26, 27-33 all write out entire proof for #27-33

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